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1.8 Integration

1.8 Integration

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Question 261
a.

Use the substitution x=3sin⁡ux = 3 \sin ux=3sinu to show that

∫01.52x+3(9−x2)32 dx=∫0p(23sec⁡utan⁡u+13sec⁡2u) du \int_{0}^{1.5} \frac{2x+3}{(9-x^2)^{\frac{3}{2}}} \, dx = \int_{0}^{p} \left( \frac{2}{3} \sec u \tan u + \frac{1}{3} \sec^2 u \right) \, du ∫01.5​(9−x2)23​2x+3​dx=∫0p​(32​secutanu+31​sec2u)du

where p p\,p is a constant to be found.

[5]
b.

Hence find the exact value of

∫01.52x+3(9−x2)32 dx \int_{0}^{1.5} \frac{2x+3}{(9-x^2)^{\frac{3}{2}}} \, dx ∫01.5​(9−x2)23​2x+3​dx
[3]
Markscheme

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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